I have been struggling with a problem, and am seeking help on the topic:
I have two dice, one with a faces and the other with b faces. Only one success can come from each die, such that the success rates of the dice are 1/a and 1/b. I want to know the expected number of times I must throw both dice to such that I obtain an n number of successes.
I know from the means of both the binomial distribution and the negative binomial distribution that I must roll die a an average of a*n times to get n successes and very similar for die b, but I can't seem to figure out how to combine the probabilities to get the answer.